@misc{BornemannYserentant, author = {Bornemann, Folkmar A. and Yserentant, Harry}, title = {A Basic Norm Equivalence for the Theory of Multilevel Methods.}, doi = {10.1007/BF01388699}, number = {SC-92-01}, abstract = {Subspace decompositions of finite element spaces based on \$L2\$-like orthogonal projections play an important role for the construction and analysis of multigrid like iterative methods. Recently several authors proved the equivalence of the associated discrete norms with the \$H^1\$-norm. The present report gives an elementary, self-contained derivation of this result which is based on the use of \$ K\$-functionals known from the theory of interpolation spaces. {\bf Keywords:} multilevel methods, nonuniform meshes, optimal convergence rates. {\bf AMS(MOS) Subject classifications:} 65N55, 65N30, 65N50.}, language = {en} }